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Mahapatra, N. R., & Dutt, S. (1997). Scalable global and local hashing strategies for duplicate pruning in parallel A  graph search. IEEE Transactions on Parallel and Distributed Systems, 8(7), 738--756.

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Isoefficiency and the Parallel Descartes Method - Decker, Krandick   (Correct)

....isoefficiency relates the number of processors and the sequential computing time necessary to maintain a given efficiency. The concept was never rigorously defined but, nevertheless, used in the analysis of a number of algorithms (Kumar Singh, 1991; Gupta Kumar, 1993; Gupta et al. 1997; Mahapatra Dutt, 1997; Yang Lin, 1997) In these applications, isoefficiency is characterized as follows. If e is a given efficiency and I e (P ) is the isoefficiency function then, for all x and P , T (x; 1) I e (P ) implies E(x; P ) e. This property does not suffice to define I e (P ) since there may be inputs ....

Mahapatra, N. R., & Dutt, S. (1997). Scalable global and local hashing strategies for duplicate pruning in parallel A  graph search. IEEE Transactions on Parallel and Distributed Systems, 8(7), 738--756.


State-of-the-Art in Parallel Search Techniques for Discrete.. - Grama, Kumar   (Correct)

....equalization, ensures that the best nodes available globally are evenly distributed across the heaps. Since the quality of the nodes changes as computation proceeds, quality equalization must be performed periodically. A variety of triggers and mechanisms have been used for quality equalization [30, 6, 45, 4]. A simple triggering mechanism tracks the best node in the system. The best node in the local heap is compared to the best node in the system and if it is considerably worse, an equalization process is initiated. Alternately, an equalization process may be initiated periodically. Quality ....

....these schemes are capable of providing linearly increasing speedups with number of processors if the problem size is increased appropriately. Specifically, scalable parallel formulations of best first tree search with isoefficiency of O(p log 2 p) on hypercube architectures have been developed [30]. Using these schemes, speedups in excess of 950 have been demonstrated on 1024 processor hypercubes in the context of TSPs formulated as best first tree search problems [6] Best First Search of State Space Graphs Efficient parallel implementation of BFS on state space graphs requires a ....

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N. R. Mahapatra and S. Dutt. Scalable global and local hashing strategies for duplicate pruning in parallel a* graph search. IEEE Trans. Parallel and Distributed Systems, 8(7), July 1997. 13


Load Balancing for Parallel Optimization Techniques - Grama, Kumar   (Correct)

....the closed list is truly randomized, this has the effect of load balancing using randomized allocation. Furthermore, since nodes are randomly allocated to processors, there is a probabilistic quality equalization for heuristic search techniques. These schemes have been studied by many researchers [15, 14]. Assuming a perfectly random hash function, it has been shown that if the number of nodes originating at each processor grows as O(log p) then each processor will have asymptotically equal number of nodes after the hash operation [15] Since each node is associated with a communication, this ....

N. R. Mahapatra and S. Dutt. Scalable global and local hashing strategies for duplicate pruning in parallel a* graph search. IEEE Trans. Parallel and Distributed Systems, 8(7), July 1997.

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